My preference was always private events because you can use existing staff and not have to transport anything to and from the restaurant.
Catering to me is a pain in the ass because you'll need additional staffing plus additional equipment for plating, holding, cooking, etc. etc. If you try to use existing staffing, the restaurant will then suffer because you'll be stretched too thin. Maybe for smaller, off-site events this would work but then you have to ask yourself if it's truly worth it.
Depending on your restaurant type and clientele, that would determine what sort of private events you would do. Buy-outs are always nice, but you'll need someone to promote or at least cold-call local companies to inquire and/or make offers. You should also talk to your sales reps from whoever your liquor distributors are, and discuss the possibility of wine/sake/beer tasting dinners.
Outside of that, social media is your friend. Heavily utilize IG, FB, Yelp, etc. to get your restaurant and photos of your food out there where everyone can see it.